cosa=4cos^3a/3-3cosa/3
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L.H.S = cos3A
= cos(2A+A)
= cos2A.cosA – sin2A.sinA
= (2cos2A - 1)cosA – 2sinA cosA sinA
= 2cos3A – cosA – 2cosA(1-cos2A)
= 2cos3A – cosA – 2cosA + 2cos3A
= 4cos3A – 3cosA
= R.H.S.
Hence Verified
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